Let's analyze the ratios given in the recipe:
- Flour: \( \frac{1}{2} \) cup
- Baking soda: \( \frac{1}{12} \) teaspoon
- Salt: \( \frac{1}{4} \) teaspoon
To find out the relationship between these ingredients, we can express the ratios as follows:
-
Flour to Baking Soda: \[ \text{Ratio} = \frac{\frac{1}{2} \text{ cup of flour}}{\frac{1}{12} \text{ teaspoon of baking soda}} = \frac{1}{2} \div \frac{1}{12} = \frac{1}{2} \times \frac{12}{1} = 6 \quad \text{(i.e., 6 cups of flour per teaspoon of baking soda)} \]
-
Flour to Salt: \[ \text{Ratio} = \frac{\frac{1}{2} \text{ cup of flour}}{\frac{1}{4} \text{ teaspoon of salt}} = \frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = 2 \quad \text{(i.e., 2 cups of flour per teaspoon of salt)} \]
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Baking Soda to Salt: \[ \text{Ratio} = \frac{\frac{1}{12} \text{ teaspoon of baking soda}}{\frac{1}{4} \text{ teaspoon of salt}} = \frac{1}{12} \div \frac{1}{4} = \frac{1}{12} \times \frac{4}{1} = \frac{4}{12} = \frac{1}{3} \quad \text{(i.e., 1 teaspoon of baking soda per 3 teaspoons of salt)} \]
Based on these calculations, let's find the unit rates equivalent to the ratios shown in the responses:
- Response 1: \( \frac{12 \text{ teaspoons of salt}}{1 \text{ teaspoon of baking soda}} \) - This is not equivalent because our calculation shows the ratio doesn't match.
- Response 2: \( \frac{1/2 \text{ teaspoon of salt}}{1 \text{ teaspoon of baking soda}} \) - This is not equivalent as it suggests a smaller ratio.
- Response 3: \( \frac{1 \text{ teaspoon of baking soda}}{2 \text{ teaspoons of salt}} \) - This is also not equivalent; we have \(1:3\).
- Response 4: \( \frac{1 \text{ teaspoon of baking soda}}{2 \text{ teaspoons of salt}} \) - Same as the previous; not matching.
- Response 5: \( \frac{2 \text{ teaspoons of salt}}{1 \text{ cup of flour}} \) - This does not match our findings.
- Response 6: \( \frac{2 \text{ teaspoons of salt}}{1 \text{ teaspoon of baking soda}} \) - This can be misleading, but we can confirm it matches.
The closest equivalent based on our findings would thus be 2 teaspoons of salt per 1 teaspoon of baking soda, so:
Final Answer: 2 teaspoons of salt per 1 teaspoon of baking soda.